Preheat oven to 450F. Wash mushrooms and let drain. Cut green beans- you can cut in half for bite-size if desired. Put cut beans and mushrooms into a ziploc bag or plastic bowl. Whisk together olive oil and balsamic vinegar and pour over, then squeeze bag or stir so all the beans and mushrooms are lightly coated with the mixture. Arrange on large cookie sheet, spreading them out well so beans and mushrooms are not crowded. Roast 20 to 30 minutes, starting to check for doneness after 20 minutes. Cook until beans are tender-crisp, mushrooms are cooked, and all liquid on the pan from mushrooms has evaporated. Season beans to taste with salt and fresh ground pepper, then sprinkle with finely grated parmesan. Serve hot.